The Chern number inequality for minimal varieties

In this talk, I will discuss the Chern number inequality on minimal varieties of general type which may have canonical singularities of complex codimension at least 3. This inequality extends the famous Bogomolov-Miyaoka-Yau inequality for smooth manifolds. I will also exam the case when the equality holds and show a new uniformization theorem for singular varieties. This is a joint work with B. Wang.